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In this paper, we propose a novel diffusion robust variable step-size least mean square (DRVSS-LMS) algorithm that is insensitive to impulsive noise for distributed estimation in the network. Conventional diffusion least mean square algorithms are based on the assumption that the background noise obeys Gaussian distribution. However, the performances of these algorithms are severely degraded when impulsive noises occur in the network. By introducing the Huber objective function which can significantly suppress the effect of impulsive noise on estimation performances, we introduce a novel method to respectively deal with the abnormal nodes carrying data contaminated by impulsive noise and the normal nodes without being contaminated by impulsive noise. In addition, the proposed algorithm is assigned with variable step-sizes to further improve the performances of distributed estimation. Simulation results show that the proposed DRVSS-LMS algorithm can achieve both higher convergence rate and lower steady-state misadjustment than several existing robust diffusion LMS algorithms in the presence of impulsive noise.

Diffusion Robust Variable Step-Size LMS Algorithm Over Distributed Networks